87564960 has 432 divisors, whose sum is σ = 373090536. Its totient is φ = 18579456.

The previous prime is 87564959. The next prime is 87565031. The reversal of 87564960 is 6946578.

87564960 is a `hidden beast` number, since 87 + 564 + 9 + 6 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 80784144 + 6780816 = 8988^2 + 2604^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 1199484 + ... + 1199556.

Almost surely, 2^87564960 is an apocalyptic number.

87564960 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 87564960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (186545268).

87564960 is an abundant number, since it is smaller than the sum of its proper divisors (285525576).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

87564960 is a wasteful number, since it uses less digits than its factorization.

87564960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 125 (or 107 counting only the distinct ones).

The product of its (nonzero) digits is 362880, while the sum is 45.

The square root of 87564960 is about 9357.6150807778. The cubic root of 87564960 is about 444.0618370168.

The spelling of 87564960 in words is "eighty-seven million, five hundred sixty-four thousand, nine hundred sixty".